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Low Rank Approximation

Ivan Markovsky

Author : Ivan Markovsky
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 44,7 Mb
Release : 2011-11-19
Category : Technology & Engineering
ISBN : 9781447122272

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Low Rank Approximation by Ivan Markovsky Pdf

Data Approximation by Low-complexity Models details the theory, algorithms, and applications of structured low-rank approximation. Efficient local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. Much of the text is devoted to describing the applications of the theory including: system and control theory; signal processing; computer algebra for approximate factorization and common divisor computation; computer vision for image deblurring and segmentation; machine learning for information retrieval and clustering; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; and psychometrics for factor analysis. Software implementation of the methods is given, making the theory directly applicable in practice. All numerical examples are included in demonstration files giving hands-on experience and exercises and MATLAB® examples assist in the assimilation of the theory.

Low-Rank Approximation

Ivan Markovsky

Author : Ivan Markovsky
Publisher : Springer
Page : 0 pages
File Size : 42,9 Mb
Release : 2019-01-10
Category : Technology & Engineering
ISBN : 3030078175

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Low-Rank Approximation by Ivan Markovsky Pdf

This book is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory with a range of applications from systems and control theory to psychometrics being described. Special knowledge of the application fields is not required. The second edition of /Low-Rank Approximation/ is a thoroughly edited and extensively rewritten revision. It contains new chapters and sections that introduce the topics of: • variable projection for structured low-rank approximation;• missing data estimation;• data-driven filtering and control;• stochastic model representation and identification;• identification of polynomial time-invariant systems; and• blind identification with deterministic input model. The book is complemented by a software implementation of the methods presented, which makes the theory directly applicable in practice. In particular, all numerical examples in the book are included in demonstration files and can be reproduced by the reader. This gives hands-on experience with the theory and methods detailed. In addition, exercises and MATLAB^® /Octave examples will assist the reader quickly to assimilate the theory on a chapter-by-chapter basis. “Each chapter is completed with a new section of exercises to which complete solutions are provided.” Low-Rank Approximation (second edition) is a broad survey of the Low-Rank Approximation theory and applications of its field which will be of direct interest to researchers in system identification, control and systems theory, numerical linear algebra and optimization. The supplementary problems and solutions render it suitable for use in teaching graduate courses in those subjects as well.

Handbook of Variational Methods for Nonlinear Geometric Data

Philipp Grohs,Martin Holler,Andreas Weinmann

Author : Philipp Grohs,Martin Holler,Andreas Weinmann
Publisher : Springer Nature
Page : 701 pages
File Size : 45,9 Mb
Release : 2020-04-03
Category : Mathematics
ISBN : 9783030313517

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Handbook of Variational Methods for Nonlinear Geometric Data by Philipp Grohs,Martin Holler,Andreas Weinmann Pdf

This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.

Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics

Felix Fritzen,David Ryckelynck

Author : Felix Fritzen,David Ryckelynck
Publisher : MDPI
Page : 254 pages
File Size : 54,6 Mb
Release : 2019-09-18
Category : Technology & Engineering
ISBN : 9783039214099

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Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics by Felix Fritzen,David Ryckelynck Pdf

The use of machine learning in mechanics is booming. Algorithms inspired by developments in the field of artificial intelligence today cover increasingly varied fields of application. This book illustrates recent results on coupling machine learning with computational mechanics, particularly for the construction of surrogate models or reduced order models. The articles contained in this compilation were presented at the EUROMECH Colloquium 597, « Reduced Order Modeling in Mechanics of Materials », held in Bad Herrenalb, Germany, from August 28th to August 31th 2018. In this book, Artificial Neural Networks are coupled to physics-based models. The tensor format of simulation data is exploited in surrogate models or for data pruning. Various reduced order models are proposed via machine learning strategies applied to simulation data. Since reduced order models have specific approximation errors, error estimators are also proposed in this book. The proposed numerical examples are very close to engineering problems. The reader would find this book to be a useful reference in identifying progress in machine learning and reduced order modeling for computational mechanics.

Low-Rank Approximation

Ivan Markovsky

Author : Ivan Markovsky
Publisher : Springer
Page : 272 pages
File Size : 51,5 Mb
Release : 2018-08-03
Category : Technology & Engineering
ISBN : 9783319896205

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Low-Rank Approximation by Ivan Markovsky Pdf

This book is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory with a range of applications from systems and control theory to psychometrics being described. Special knowledge of the application fields is not required. The second edition of /Low-Rank Approximation/ is a thoroughly edited and extensively rewritten revision. It contains new chapters and sections that introduce the topics of: • variable projection for structured low-rank approximation;• missing data estimation;• data-driven filtering and control;• stochastic model representation and identification;• identification of polynomial time-invariant systems; and• blind identification with deterministic input model. The book is complemented by a software implementation of the methods presented, which makes the theory directly applicable in practice. In particular, all numerical examples in the book are included in demonstration files and can be reproduced by the reader. This gives hands-on experience with the theory and methods detailed. In addition, exercises and MATLAB^® /Octave examples will assist the reader quickly to assimilate the theory on a chapter-by-chapter basis. “Each chapter is completed with a new section of exercises to which complete solutions are provided.” Low-Rank Approximation (second edition) is a broad survey of the Low-Rank Approximation theory and applications of its field which will be of direct interest to researchers in system identification, control and systems theory, numerical linear algebra and optimization. The supplementary problems and solutions render it suitable for use in teaching graduate courses in those subjects as well.

Generalized Low Rank Models

Madeleine Udell,Corinne Horn,Reza Zadeh,Stephen Boyd

Author : Madeleine Udell,Corinne Horn,Reza Zadeh,Stephen Boyd
Publisher : Unknown
Page : 142 pages
File Size : 42,8 Mb
Release : 2016-05-03
Category : Electronic
ISBN : 1680831402

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Generalized Low Rank Models by Madeleine Udell,Corinne Horn,Reza Zadeh,Stephen Boyd Pdf

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well-known techniques in data analysis, such as nonnegative matrix factorization, matrix completion, sparse and robust PCA, k-means, k-SVD, and maximum margin matrix factorization. The method handles heterogeneous data sets, and leads to coherent schemes for compressing, denoising, and imputing missing entries across all data types simultaneously. It also admits a number of interesting interpretations of the low rank factors, which allow clustering of examples or of features. We propose several parallel algorithms for fitting generalized low rank models, and describe implementations and numerical results.

Spectral Algorithms

Ravindran Kannan,Santosh Vempala

Author : Ravindran Kannan,Santosh Vempala
Publisher : Now Publishers Inc
Page : 153 pages
File Size : 50,7 Mb
Release : 2009
Category : Computers
ISBN : 9781601982742

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Spectral Algorithms by Ravindran Kannan,Santosh Vempala Pdf

Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well as "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, and novel algorithms for estimating spectral parameters. The first part of the book presents applications of spectral methods to problems from a variety of topics including combinatorial optimization, learning and clustering. The second part of the book is motivated by efficiency considerations. A feature of many modern applications is the massive amount of input data. While sophisticated algorithms for matrix computations have been developed over a century, a more recent development is algorithms based on "sampling on the fly" from massive matrices. Good estimates of singular values and low rank approximations of the whole matrix can be provably derived from a sample. The main emphasis in the second part of the book is to present these sampling methods with rigorous error bounds. It also presents recent extensions of spectral methods from matrices to tensors and their applications to some combinatorial optimization problems.

Low-Rank Semidefinite Programming

Alex Lemon,Anthony Man-Cho So,Yinyu Ye

Author : Alex Lemon,Anthony Man-Cho So,Yinyu Ye
Publisher : Now Publishers
Page : 180 pages
File Size : 42,5 Mb
Release : 2016-05-04
Category : Mathematics
ISBN : 1680831364

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Low-Rank Semidefinite Programming by Alex Lemon,Anthony Man-Cho So,Yinyu Ye Pdf

Finding low-rank solutions of semidefinite programs is important in many applications. For example, semidefinite programs that arise as relaxations of polynomial optimization problems are exact relaxations when the semidefinite program has a rank-1 solution. Unfortunately, computing a minimum-rank solution of a semidefinite program is an NP-hard problem. This monograph reviews the theory of low-rank semidefinite programming, presenting theorems that guarantee the existence of a low-rank solution, heuristics for computing low-rank solutions, and algorithms for finding low-rank approximate solutions. It then presents applications of the theory to trust-region problems and signal processing.

Exact and Approximate Modeling of Linear Systems

Ivan Markovsky,Jan C. Willems,Sabine Van Huffel,Bart De Moor

Author : Ivan Markovsky,Jan C. Willems,Sabine Van Huffel,Bart De Moor
Publisher : SIAM
Page : 210 pages
File Size : 50,7 Mb
Release : 2006-01-31
Category : Mathematics
ISBN : 9780898716030

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Exact and Approximate Modeling of Linear Systems by Ivan Markovsky,Jan C. Willems,Sabine Van Huffel,Bart De Moor Pdf

Exact and Approximate Modeling of Linear Systems: A Behavioral Approach elegantly introduces the behavioral approach to mathematical modeling, an approach that requires models to be viewed as sets of possible outcomes rather than to be a priori bound to particular representations. The authors discuss exact and approximate fitting of data by linear, bilinear, and quadratic static models and linear dynamic models, a formulation that enables readers to select the most suitable representation for a particular purpose. This book presents exact subspace-type and approximate optimization-based identification methods, as well as representation-free problem formulations, an overview of solution approaches, and software implementation. Readers will find an exposition of a wide variety of modeling problems starting from observed data. The presented theory leads to algorithms that are implemented in C language and in MATLAB.

Low-rank Approximation

Ivan Markovsky

Author : Ivan Markovsky
Publisher : Unknown
Page : 128 pages
File Size : 44,7 Mb
Release : 2019
Category : MATHEMATICS
ISBN : 3319896210

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Low-rank Approximation by Ivan Markovsky Pdf

This book is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory with a range of applications from systems and control theory to psychometrics being described. Special knowledge of the application fields is not required. The second edition of /Low-Rank Approximation/ is a thoroughly edited and extensively rewritten revision. It contains new chapters and sections that introduce the topics of: • variable projection for structured low-rank approximation; • missing data estimation; • data-driven filtering and control; • stochastic model representation and identification; • identification of polynomial time-invariant systems; and • blind identification with deterministic input model. The book is complemented by a software implementation of the methods presented, which makes the theory directly applicable in practice. In particular, all numerical examples in the book are included in demonstration files and can be reproduced by the reader. This gives hands-on experience with the theory and methods detailed. In addition, exercises and MATLAB^® /Octave examples will assist the reader quickly to assimilate the theory on a chapter-by-chapter basis. "Each chapter is completed with a new section of exercises to which complete solutions are provided." Low-Rank Approximation (second edition) is a broad survey of the Low-Rank Approximation theory and applications of its field which will be of direct interest to researchers in system identification, control and systems theory, numerical linear algebra and optimization. The supplementary problems and solutions render it suitable for use in teaching graduate courses in those subjects as well.

SVD and Signal Processing, III

M. Moonen,B. De Moor

Author : M. Moonen,B. De Moor
Publisher : Elsevier
Page : 485 pages
File Size : 45,6 Mb
Release : 1995-03-16
Category : Technology & Engineering
ISBN : 0080542158

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SVD and Signal Processing, III by M. Moonen,B. De Moor Pdf

Matrix Singular Value Decomposition (SVD) and its application to problems in signal processing is explored in this book. The papers discuss algorithms and implementation architectures for computing the SVD, as well as a variety of applications such as systems and signal modeling and detection. The publication presents a number of keynote papers, highlighting recent developments in the field, namely large scale SVD applications, isospectral matrix flows, Riemannian SVD and consistent signal reconstruction. It also features a translation of a historical paper by Eugenio Beltrami, containing one of the earliest published discussions of the SVD. With contributions sourced from internationally recognised scientists, the book will be of specific interest to all researchers and students involved in the SVD and signal processing field.

Symbolic-Numeric Computation

Dongming Wang,Li-Hong Zhi

Author : Dongming Wang,Li-Hong Zhi
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 52,8 Mb
Release : 2007-01-22
Category : Mathematics
ISBN : 9783764379834

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Symbolic-Numeric Computation by Dongming Wang,Li-Hong Zhi Pdf

The growing demand of speed, accuracy, and reliability in scientific and engineering computing has been accelerating the merging of symbolic and numeric computations. These two types of computation coexist in mathematics yet are separated in traditional research of mathematical computation. This book presents 27 research articles on the integration and interaction of symbolic and numeric computation.

Low-Rank and Sparse Modeling for Visual Analysis

Yun Fu

Author : Yun Fu
Publisher : Springer
Page : 236 pages
File Size : 41,6 Mb
Release : 2014-10-30
Category : Computers
ISBN : 9783319120003

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Low-Rank and Sparse Modeling for Visual Analysis by Yun Fu Pdf

This book provides a view of low-rank and sparse computing, especially approximation, recovery, representation, scaling, coding, embedding and learning among unconstrained visual data. The book includes chapters covering multiple emerging topics in this new field. It links multiple popular research fields in Human-Centered Computing, Social Media, Image Classification, Pattern Recognition, Computer Vision, Big Data, and Human-Computer Interaction. Contains an overview of the low-rank and sparse modeling techniques for visual analysis by examining both theoretical analysis and real-world applications.

Sketching as a Tool for Numerical Linear Algebra

David P. Woodruff

Author : David P. Woodruff
Publisher : Now Publishers
Page : 168 pages
File Size : 44,7 Mb
Release : 2014-11-14
Category : Computers
ISBN : 168083004X

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Sketching as a Tool for Numerical Linear Algebra by David P. Woodruff Pdf

Sketching as a Tool for Numerical Linear Algebra highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compressed it to a much smaller matrix by multiplying it by a (usually) random matrix with certain properties. Much of the expensive computation can then be performed on the smaller matrix, thereby accelerating the solution for the original problem. It is an ideal primer for researchers and students of theoretical computer science interested in how sketching techniques can be used to speed up numerical linear algebra applications.

Mining of Massive Datasets

Jure Leskovec,Anand Rajaraman,Jeffrey David Ullman

Author : Jure Leskovec,Anand Rajaraman,Jeffrey David Ullman
Publisher : Cambridge University Press
Page : 480 pages
File Size : 40,9 Mb
Release : 2014-11-13
Category : Computers
ISBN : 9781107077232

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Mining of Massive Datasets by Jure Leskovec,Anand Rajaraman,Jeffrey David Ullman Pdf

Now in its second edition, this book focuses on practical algorithms for mining data from even the largest datasets.

Low Rank Approximation

Low Rank Approximation by Ivan Markovsky Pdf

Low-Rank Approximation by Ivan Markovsky Pdf

Handbook of Variational Methods for Nonlinear Geometric Data by Philipp Grohs,Martin Holler,Andreas Weinmann Pdf

Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics by Felix Fritzen,David Ryckelynck Pdf

Low-Rank Approximation by Ivan Markovsky Pdf

Generalized Low Rank Models by Madeleine Udell,Corinne Horn,Reza Zadeh,Stephen Boyd Pdf

Spectral Algorithms by Ravindran Kannan,Santosh Vempala Pdf

Low-Rank Semidefinite Programming by Alex Lemon,Anthony Man-Cho So,Yinyu Ye Pdf

Exact and Approximate Modeling of Linear Systems by Ivan Markovsky,Jan C. Willems,Sabine Van Huffel,Bart De Moor Pdf

Low-rank Approximation by Ivan Markovsky Pdf

SVD and Signal Processing, III by M. Moonen,B. De Moor Pdf

Symbolic-Numeric Computation by Dongming Wang,Li-Hong Zhi Pdf

Low-Rank and Sparse Modeling for Visual Analysis by Yun Fu Pdf

Sketching as a Tool for Numerical Linear Algebra by David P. Woodruff Pdf

Mining of Massive Datasets by Jure Leskovec,Anand Rajaraman,Jeffrey David Ullman Pdf

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